77
T
ABLE
O
F
F
IGURES
Figure 1: Original Image ................................................................................................................................ 6
Figure 2: Cropped Image ............................................................................................................................... 7
Figure 3: Scaled Images (Up and Down) ........................................................................................................ 7
Figure 4: Image Rotated 90
o
Right ................................................................................................................ 8
Figure 5: Blurred Image ................................................................................................................................. 8
Figure 6: Horizontally Reflected Image ......................................................................................................... 9
Figure 7: Auto-Contrasted Image ................................................................................................................ 10
Figure 8: Lighter and Darker Images ........................................................................................................... 11
Figure 9: Horizontally Sheared Image ......................................................................................................... 11
Figure 10: Harris Corner Detector .............................................................................................................. 13
Figure 11: Autocorrelation Function Graphical Representation ................................................................ 15
Figure 12: Classification of Image Points Based on Response Size Using the Eigenvalues of M ................ 15
Figure 13: Harris Corner Point Detection Workflow .................................................................................. 17
Figure 14: Rotation Invariance
.................................................................................................................... 18
Figure 15: The Harris Corner Detector is Not Invariant to Image Scaling
................................................... 18
Figure 16: Partial Invariance to Affine Intensity Change
........................................................................... 19
Figure 17: Graph (G) Example ..................................................................................................................... 23
Figure 18: Example of Walk, Trail, Path, and Cycles.................................................................................... 24
Figure 19: A Directed Graph ........................................................................................................................ 25
Figure 20: The Cube Graph; Edge Crossing; Planar Representation .......................................................... 26
Figure 21: Faces of a Graph ........................................................................................................................ 27
Figure 22: Dual Graphs ................................................................................................................................ 27
Figure 23: Contracting edge v
1
v
2
to vertex ` ............................................................................................... 30
Figure 24: Graph Coloring Examples with χ = 3 ........................................................................................... 30
Figure 25: Graph Diameter Example .......................................................................................................... 31
Figure 26: Graph G
1
Representations .......................................................................................................... 32
Figure 27: Graph G
2
Representations .......................................................................................................... 32
Figure 28: Voronoi Diagram ....................................................................................................................... 38
Figure 29: Delaunay Triangulation ............................................................................................................. 40
Figure 30: An Example of Voronoi Diagram Creation ................................................................................. 43
Figure 31: The Values for the Coorfinates of the Generating Set of Figure 30 ........................................... 44
Figure 32: Vertice and Cell Arrays for the Voronoi Diagram in Figure 30 ................................................... 45
Figure 33: Delaunay Triangulation of the Points from Figure 30-left ......................................................... 46
Figure 34: Harris Corner Points Parameter Selection Window ................................................................... 48
Figure 35: Voronoi Diagrams (a) with threshold 5,000; (b) with threshold 15,000 .................................... 50
Figure 36: Steps in Obtaining a Graph from an Image ................................................................................ 57
Figure 37: Other Representation of the Delaunay Graph ........................................................................... 58
Figure 38: Original Image ............................................................................................................................ 61
Figure 39: Corner Points .............................................................................................................................. 61
Figure 40: Voronoi Diagram ........................................................................................................................ 61